Final answer:
The velocity of the object is zero at t = 0 and at t = 1 second, based on the given velocity-time relationship and equation v(t) = 5t(1 - t).
Step-by-step explanation:
The velocity of the object is given to be 0 m/s at t = 0 seconds. Given the velocity-time relationship described, we can infer that the object's velocity will be zero at other points in time if the graph of the velocity indicates so. The graph shows that from t = 0 to t = 0.7 seconds, the ball's horizontal velocity is a constant positive value. Therefore, within this interval, the velocity is never zero after t = 0.
However, from the given equations, the velocity equation v(t) = 5t(1 - t) specifies that the velocity is zero when t is equal to 1 second. This is derived from the equation by setting v(t) to 0 and solving for t, yielding the solutions t = 0 and t = 1 second. As there is no other information suggesting other points in time where velocity is zero, we can conclude that the velocity of the object is zero at t = 0 and t = 1 second.